Steps

Method1

Early in the game

Place them far enough apart that the city's borders will not expand into another's but not so far away that it will be inaccessible from your capitol.

3

Make all your Great Artists join your cities as Super Specialists.

Method2

When next to opponents

1

Use a "cultural bomb".

2

Take one or two great artists to a city next to the areas you want to expand and have them join as Super Specialists. This will usually expand your territory in one turn and sometimes, if the cultural flip is on, make a city become yours without fighting at all!